It looks like I have resolved this issue by deleting the following files and restarting:
FWIW... I first deleted the files from the ~/Library/Preferences/ByHost folder and then restarted. The issue persisted. I then found and deleted the MobileMeAccounts files from ~/Library/Preferences and restarted and the messages no longer appear in Console for me.
It appears to be completely resolved (finally)...
I deleted the ~/Library/Prefernces/MobileMeAccount.plist again. Then I additionally deleted these files:
Then restarted, opened Mail, Contacts (formally Address Book), Calendar (formally iCal) and Messages (fromally iChat). All applications continues to work properly using my Apple ID settings and the messages no longer appear in Console.